Comprehensive survival analysis of breast cancer patients: a bayesian network approach

Breast cancer is recognized as one of the leading causes of cancer-related deaths globally. A deeper understanding of the complex interactions between clinical, pathological, and treatment-related factors is essential for improving patient outcomes.

Following comprehensive data cleaning and preprocessing, an analysis was performed on a cohort of 1,980 primary breast cancer samples from the METABRIC database. The dataset was divided into a 75/25 training-testing split, and five-fold cross-validation was applied to the training set to mitigate overfitting. Overall and relapse-free survival were then modeled using four fully parametric distributions: Weibull, Exponential, Log-Normal, and Log-Logistic, along with their corresponding Accelerated Failure Time (AFT) forms, to identify significant prognostic features. Competing models were ranked by the Akaike Information Criterion (AIC) and further validated through Quantile-Quantile (QQ) plots. Finally, the probabilistic relationships among the significant factors selected by the optimal AFT models were explored using a Bayesian Belief Network (BBN), whose structure was learned from the training data using multiple score-based algorithms and refined through expert-driven judgment; all conditional probability parameters were estimated using maximum likelihood.

The Weibull model provided the best fit for overall survival, whereas the Log-Normal form was optimal for relapse-free survival, each satisfying their respective error-distribution diagnostics. In the hold-out test set, the Bayesian network achieved an Area Under the Curve (AUC) of 0.880 and an F1-score of 0.779. Age at diagnosis, menopausal status, tumor stage, lymph-node burden, and treatment modality were identified as the most influential predictors, and the learned network clarified their direct and mediated effects on both survival endpoints.

Through the integration of validated parametric survival models with a data-driven BBN, this study delivers a comprehensive framework for estimating individualized survival probabilities and visualizing the complex probabilistic relationships that characterize high-risk cancer patient profiles. This approach supports evidence-based, personalized breast cancer management and demonstrates the potential for guiding clinical decision-making and adapting to diverse external patient cohorts.